How to circumscribe a cilinder around an irregular shape using edges of irregular shape?
I would recommend adding a new cylinder with more sides in this case.

Press Shift+A to add a new object, and select Mesh > Cylinder.

Before you click or do anything else, you should see a small collapsed box in the bottom left corner labelled Add Cylinder. Expand it, and change the number of vertices (first option).

If you're looking for a good beginner tutorial series, I would recommend you follow the Donut Tutorial Series by BlenderGuru.

Edit:

Here's a lengthier method if you want to build off the starting mesh.

If you want to keep the original shape, first duplicate it then work off of the new object.

With the object selected, Tab into edit mode. Press 2 to enter edge select mode, and while holding Shift+Alt, click on one of the horizontal edges on the top, and bottom. This should have selected the top/bottom edge loops.



Now, right-click (or left, if you're using right-click select), and select Subdivide at the top of the menu that pops up. This will add additional vertical cuts in the middle of all the faces.

Now, hold Ctrl+Alt and select one of the original vertical edges. This should select all the vertical edges. Next, go to the Select drop-down menu in the top left corner, and select Checker Deselect. Now only the newly added edges should be selected.

Now, you can press S to scale, then Shift+Z to scale in XY axes only. Scale it up a bit, and there you go, the mesh is closer to a cylinder. If you want a clearer view of the mesh while scaling, press 7 on the Numpad to enter the top orthographic view.

If you wish to add even more sides, you can repeat this process.

If you're looking for a smoothly shaded cylinder, follow the process below.

In edit mode, select the top and bottom edge loops using the same shortcut as before, then right-click and select Mark Seam. Then, Tab back out into object mode, right-click and select Shade Smooth.

The last thing you will need to do is to go to the Object Properties tab (the icon is a green triangle with squares on each corner), and go to Normals > Auto-smooth. Enable auto-smooth.

This is the result using one iteration of subdividing the surface.